Profitlessly is the adverb: you do something in a profitless way. You may work profitlessly (no money comes back), or wait profitlessly (nothing useful happens). The meaning is the same pair as profitless — no profit, or no real use — only now it tells you how the action went. It is quite formal. In ordinary talk people say without making any money, for nothing, or pointlessly. You will meet this more in writing than in the street.